We will focus primarily on sequential approaches to persistent homology computation. Other, non-sequential approaches include the chunk algorithm [1]}, spectral sequence procedures [2]}, [3]}, Morse-theoretic batch reduction [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, distributed algorithms [13]}, [14]}, [15]}, GPU acceleration [16]}, [17]}, streaming [18]}, and homotopy collapse [19]}, [20]}, [21]}.
There are closely related techniques in matrix factorization and zigzag persistence [22]}, [23]}, [24]}.
